Recursive Clifford noise reduction

TL;DR

This paper introduces a recursive Clifford noise reduction method that significantly lowers logical error rates in large circuits with minimal additional qubits and gates, promising improved error correction in quantum computing.

Contribution

The paper presents a recursive extension of CliNR that enhances error reduction capabilities for larger circuits with low overhead, advancing quantum error correction techniques.

Findings

Recursive CliNR reduces logical error rates more effectively for large circuits.

The method requires modest qubit and gate overheads.

Numerical simulations show advantages in near-term quantum devices.

Abstract

Clifford noise reduction (CliNR) is a partial error correction scheme that reduces the logical error rate of Clifford circuits at the cost of a modest qubit and gate overhead. The CliNR implementation of an $n$-qubit Clifford circuit of size $s$ achieves a vanishing logical error rate if $snp^2\rightarrow 0$ where $p$ is the physical error rate. Here, we propose a recursive version of CliNR that can reduce errors on larger circuits with a relatively small gate overhead. When $np \rightarrow 0$, the logical error rate can be vanishingly small. This implementation requires $\left(2\left\lceil \log(sp)\right\rceil+3\right)n+1$ qubits and at most $24 s \left\lceil(sp)^4\right\rceil $ gates. Using numerical simulations, we show that the recursive method can offer an advantage in a realistic near-term parameter regime. When circuit sizes are large enough, recursive CliNR can reach a lower logical error rate than the original CliNR with the same gate overhead. The results offer promise for reducing logical errors in large Clifford circuits with relatively small overheads.